Finite Group Databasebeta

C2×#22558060 #30745512

order17152
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#22558060

Splittings

SylowC67 ⋊ C2×#1283

Subgroups

subgroupG/H
centerC22×C4(C2×D67)⋊C4
commutatorC22×C67C2×C4×C8
FrattiniC2×C42C22×D67
FittingC2×C4×M16×C67C2
socleC23×C67#95
prime radicalC24×C67C42
cosocleC2×C42×C67C23
hypercenterC2×C4×M16D67
hypocenterC67C2×#1283
LCSG ▷ C22×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×M16

722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2728 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 59249);